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Then answer the following questions regarding Hessian matrices and their characteristic roots.(a) Which of Probs. 1 through 4 yield diagonal Hessian matrices? In each such case, do the diagonal elements possess a uniform sign?(b) What can you conclude about the characteristic roots of each diagonal Hessian matrix found? About the sign definiteness of d^2 z ?(c) Do the results of the characteristic-root test check with those of the determinantal test?